Question: What's the first wrong statement in the proof below that $ \triangle CAB \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \overline{BD} \cong \overline{BC}$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ $ \angle CEF \cong \angle BAC$ $, \ $ and $\ $ $ \angle ECF \cong \angle ACB$ Proof $ \triangle CAB \cong \triangle DEB$ because SAS $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \angle BED \cong \angle CBE$ because alternate interior angles are equal $ \angle BAC \cong \angle BCE$ because corresponding parts of congruent triangles are congruent $ \triangle CAB \cong \triangle CEF$ because AAS $ \triangle CAB \cong \triangle CEB$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \angle BCE \cong \angle BAC$ is the first wrong statement.